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Lindenstrauss wins prestigious Fields Medal for mathematics work

Posted August 20, 2010; 07:02 p.m.

by Kitta MacPherson

Elon Lindenstrauss, a Princeton professor of mathematics, has received one of this year's Fields Medals, widely considered to be the math world's equivalent of the Nobel Prize.

"One of the best parts of being a mathematician is interacting with other mathematicians: there are a lot of supersmart -- also often very generous -- people in this field," Lindenstrauss said. "It is quite remarkable to be chosen to get the Fields Prize from this extraordinary pool of talent. I have spent many years in Princeton at various stages of my career, and think that the combination of the Department of Mathematics at Princeton University and the School of Mathematics at the IAS (Institute for Advanced Study) in close proximity makes it a wonderful place to do mathematics -- possibly the best place there is."

Lindenstrauss, who came to Princeton in 2004, will remain on faculty until Sept. 1, when he will join the faculty of the Hebrew University of Jerusalem in Israel. He also will work as a visiting research collaborator at Princeton for the coming year.

The awards for outstanding mathematical achievement were presented Thursday, Aug. 19, at the opening ceremony of the International Congress of Mathematicians in Hyderabad, India.

"He has a penetrating mind," said Princeton's Eugene Higgins Professor of Mathematics Peter Sarnak of his colleague. "He is charming, a very modest guy and a very deep thinker."

Lindenstrauss studies ergodic theory, dynamical systems and number theory. Ergodic theory describes the statistical and qualitative behavior of measurable group actions on mathematical constructs known as measure spaces. Originated in the 1930s by mathematicians including John von Neumann, it has grown to be of wide interest to researchers, and has applications to number theory, differential geometry, statistical mechanics and functional analysis.

In being honored with the Fields Medal, Lindenstrauss was cited for developing "extraordinarily powerful theoretical tools in ergodic theory, a field of mathematics initially developed to understand celestial mechanics. He then used them, together with his deep understanding of ergodic theory, to solve a series of striking problems in areas of mathematics that are seemingly far afield."

Sarnak said, " He has uncovered something that is far-reaching and deep. I'm sure it will be at the heart of many developments, some related and some quite unexpected."

Lindenstrauss is also known for applying ergodic theory to a longstanding problem in number theory known as the Littlewood Conjecture. In this work, he collaborated with two other mathematicians, Manfred Einsiedler of Switzerland and Anatole Katok of Penn State University. They did not solve the problem but came close.

"The problem is so notoriously difficult that everyone else who has tried it has come away with their fingers burnt and with nothing to say," Sarnak said. Lindenstrauss' work on the conjecture with the others, Sarnak said, was "spectacular."

This year's other Fields winners were Cédric Villani of the Institut Henri Poincaré in Paris, Ngo Bao Chau of the Université Paris-Sud, and Stanislav Smirnov of the Université de Genève.

After earning his Ph.D. from Hebrew University, Lindenstrauss held academic positions at the Institute for Advanced Study, Stanford University and New York University before coming to Princeton. He also was a long-term prize fellow at the Clay Mathematics Institute while serving concurrently as a visiting member of the Courant Institute at NYU. He recently won the Fermat Prize for Mathematics Research for his work in number theory.

Fields Medals are awarded every four years to mathematicians no older than 40, and two to four mathematicians can receive them each time they are presented. Canadian mathematician John Charles Fields created the medals, which were first awarded in 1936. Along with a gold medallion inscribed with the winner's name, the awards bring a cash prize of about $13,300.

At the same meeting at which Lindenstrauss received his medal, Ingrid Daubechies, the William R. Kenan, Jr. Professor of Mathematics and Applied and Computational Mathematics at Princeton, was named president of the International Mathematical Union for the term 2011-14.